Ascending HNN extensions of polycyclic groups have the same cohomology as their profinite completions

Karl Lorensen

Assume $G$ is a polycyclic group and $\varphi :G\to G$ an endomorphism. Let $G{\ast }_{\varphi }$ be the ascending HNN extension of $G$ with respect to $\varphi$; that is, $G{\ast }_{\varphi }$ is given by the present…